A hair-cutting system of the type defined in the opening paragraph is commercially available from the Applicant under the type designation HS 025 and is known therefrom. In the known hair-cutting system the hair-cutting apparatus comprises an adjustment button formed by a slide button and an on/off button also formed by a slide button. Both buttons are arranged in line with one another in the longitudinal direction of the housing at the location of the front side of the hair-cutting apparatus in the grip area of the housing, the adjustment button being disposed adjacent the coupling area, i.e. nearer the toothed cutting device of the hair-cutting apparatus and the on/off button being disposed behind it in the longitudinal direction of the housing, i.e. further away from the toothed cutting device. In the known hair-cutting system the adjustment button is simply and easily slidable between several, i.e. seven settings in total, by the thumb of the hand which holds the grip area of the hair-cutting apparatus during operation. In order to actuate the on/off button of the known hair-cutting system the thumb of the hand which holds the grip area of the hair-cutting apparatus during operation should be placed on the on/off button, after which the on/off button can be slid between its on-position and its off-position. After the on/off button has been slid, for example, into its on-position in order to switch on the motor of the hair-cutting apparatus, upon which the toothed cutting device of the hair-cutting apparatus is put into operation, the thumb should be moved to the adjustment button in order to enable a desired hair-cutting length to be adjusted, for which it is not only necessary to move the thumb but also to change the position of the entire hair-cutting apparatus in the hand holding the hair-cutting apparatus. This is a comparatively inconvenient operation, which is consequently susceptible of improvement.